IMO, basic income for parents is absolutely a policy that Japan should enact.

And the question of how much the payment should be has a straightforward answer: adjust until the birth rate reaches replacement.

If the payment ends up high enough that some mothers or fathers opt to leave the labor force to focus on raising their kids, then so be it; that's probably healthier for society in the long term.

It would be expensive, yes, but cheaper than the alternatives. And anyway, Japan's stagnant economy would likely benefit from the boost to consumer demand.